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NCERT Class 10 Mathematics – Chapter 4: Quadratic Equations
Board Exam 2026 focused online test strictly based on NCERT textbook.
- A quadratic equation is of the form ax² + bx + c = 0.
- Standard methods include factorisation and quadratic formula.
- Discriminant D = b² − 4ac determines nature of roots.
- D > 0 gives real and distinct roots.
- D = 0 gives real and equal roots.
- D < 0 gives no real roots.
Q1. The standard form of a quadratic equation is:
ax² + bx + c = 0
ax + b = 0
x² = ax + b
ax³ + bx + c = 0
NCERT defines quadratic equation in standard form.
Q2. Degree of a quadratic equation is:
1
2
3
0
Highest power of variable is 2.
Q3. Which of the following is a quadratic equation?
2x + 5 = 0
x³ − 1 = 0
x² − 7x + 10 = 0
5 = 0
Degree 2 equation.
Q4. The discriminant of ax² + bx + c = 0 is:
b² + 4ac
4ac − b²
b² + ac
b² − 4ac
D = b² − 4ac.
Q5. If D > 0, the roots are:
Real and equal
Real and distinct
Imaginary
No solution
Positive discriminant.
Q6. If D = 0, the roots are:
Real and equal
Real and distinct
Non-real
Unequal
Zero discriminant.
Q7. If D < 0, the equation has:
Two real roots
Equal roots
No real roots
One root
Negative discriminant.
Q8. Roots of x² − 9 = 0 are:
3 only
−3 only
0 and 9
3 and −3
Factorisation.
Q9. Which method is suitable for x² − 5x = 0?
Quadratic formula
Factorisation
Graphical
Trial
Common factor x.
Q10. The roots of x² = 4 are:
2 and −2
4 and −4
0 and 4
1 and −1
x = ±2.
Q11. The quadratic formula is:
(−b ± √(b² + 4ac))/2a
(b ± √(b² − 4ac))/2a
(−b ± √(b² − 4ac))/2a
(b ± √(b² + 4ac))/a
NCERT formula.
Q12. For equation 2x² + 3x + 1 = 0, value of a is:
1
3
0
2
Coefficient of x².
Q13. The product of roots of ax² + bx + c = 0 is:
c/a
a/c
−b/a
b/a
NCERT relation.
Q14. The sum of roots of ax² + bx + c = 0 is:
c/a
−b/a
b/a
a/b
Sum = −b/a.
Q15. If roots are equal, then D equals:
1
Negative
0
Positive
Equal roots when D=0.
Q16. The nature of roots depends on:
Coefficient a
Coefficient b
Constant c
Discriminant
Discriminant decides nature.
Q17. Which quadratic has roots 2 and 3?
x² − 5x + 6 = 0
x² + 5x + 6 = 0
x² − x − 6 = 0
x² + x − 6 = 0
(x−2)(x−3)=0.
Q18. If product of roots is negative, roots are:
Both positive
Of opposite signs
Both negative
Equal
Negative product implies opposite signs.
Q19. A quadratic equation always has:
One root
Three roots
Two roots
No roots
Degree 2 gives two roots.
Q20. Which method is always applicable?
Factorisation
Graphical
Trial
Quadratic formula
Formula works for all.
Q21. Roots of x² + 1 = 0 are:
No real roots
1 and −1
0 and 1
Real
D < 0.
Q22. If a = 0 in ax² + bx + c = 0, the equation becomes:
Quadratic
Linear
Cubic
Constant
Degree reduces to 1.
Q23. The equation x(x−3)=0 has roots:
−3 and 3
−3 and 0
0 and 3
1 and 3
Zero product property.
Q24. Nature of roots of x² − 4x + 4 = 0 is:
Real and distinct
No real
Complex
Real and equal
Perfect square.
Q25. The graph of a quadratic equation is a:
Parabola
Line
Circle
Hyperbola
Quadratic graphs.
Q26. If roots are 1 and −1, equation is:
x² − 1 = 0
x² − 1 = 0
x² + 1 = 0
x − 1 = 0
(x−1)(x+1)=0.
Q27. If D = 25, roots are:
Equal
Imaginary
Real and distinct
Zero
Positive D.
Q28. Which equation has equal roots?
x² − 5x + 6 = 0
x² + 1 = 0
x² − 3x + 2 = 0
x² − 4x + 4 = 0
Perfect square.
Q29. For real roots, D must be:
≥ 0
< 0
= −1
Imaginary
Non-negative.
Q30. The roots of x² − 2x − 3 = 0 are:
1 and 3
3 and −1
−3 and 1
−1 and −3
Factorisation.
Q31. If sum of roots is 0, then b equals:
a
c
0
1
−b/a=0.
Q32. Which equation has roots −2 and 5?
x² − 3x − 10 = 0
x² + 3x − 10 = 0
x² − 7x + 10 = 0
x² − 3x − 10 = 0
(x+2)(x−5)=0.
Q33. If c = 0, one root is:
0
1
−1
2
x is common factor.
Q34. The equation x² + 4x + 5 = 0 has:
Real roots
No real roots
Equal roots
One root
D<0.
Q35. If a>0, parabola opens:
Downwards
Horizontally
Upwards
Sideways
Positive a.
Q36. The roots of x² = 0 are:
1 and 0
−1 and 0
Two distinct roots
0 and 0
Equal roots.
Q37. Which term affects shape of parabola?
Coefficient a
b
c
Constant
a determines opening.
Q38. If roots are equal, graph touches x-axis at:
Two points
One point
No point
Many points
Tangential.
Q39. Which method is fastest when factorable?
Formula
Graph
Factorisation
Trial
Direct factors.
Q40. The value of D for x² − 6x + 9 = 0 is:
36
18
−36
0
b²−4ac = 36−36.
Q41. Roots of x² + 7x = 0 are:
0 and −7
7 and 0
−7 and 7
1 and 7
x(x+7)=0.
Q42. If product of roots is positive and sum negative, roots are:
Positive
Negative
Opposite
Zero
Both negative.
Q43. Which equation has roots 4 and −2?
x² − 2x − 8 = 0
x² + 2x − 8 = 0
x² − 2x − 8 = 0
x² + 8 = 0
(x−4)(x+2)=0.
Q44. The roots of x² − 1 = 0 are:
0 and 1
1 and 1
0 and −1
1 and −1
Difference of squares.
Q45. Quadratic equations arise in:
Area problems
Linear motion
Statistics
Matrices
NCERT applications.
Q46. Which value of D gives imaginary roots?
0
Negative
Positive
Zero
Negative discriminant.
Q47. If roots are α and β, then equation is:
x² + (α+β)x + αβ = 0
x² − αβx + (α+β) = 0
x² − (α+β)x + αβ = 0
x − αβ = 0
Standard relation.
Q48. If roots are 5 and 5, then equation is:
x² − 10x + 5 = 0
x² + 10x + 25 = 0
x² − 25 = 0
x² − 10x + 25 = 0
(x−5)².
Q49. The quadratic formula was derived by:
Completing the square
Factorisation
Graph
Trial
NCERT derivation.
Q50. The main aim of this chapter is to:
Study linear equations
Solve quadratic equations
Plot graphs only
Find statistics
NCERT objective.
📘 NCERT Class 10 Maths – Chapter-wise Online Tests
- Chapter 1: Real Numbers – Online Test
- Chapter 2: Polynomials – Online Test
- Chapter 3: Pair of Linear Equations in Two Variables – Online Test
- Chapter 4: Quadratic Equations – Online Test
- Chapter 5: Arithmetic Progressions – Online Test
- Chapter 6: Triangles – Online Test
- Chapter 7: Coordinate Geometry – Online Test
- Chapter 8: Introduction to Trigonometry – Online Test
- Chapter 9: Applications of Trigonometry – Online Test
- Chapter 10: Circles – Online Test
- Chapter 11: Areas Related to Circles – Online Test
- Chapter 12: Surface Areas and Volumes – Online Test
- Chapter 13: Statistics – Online Test
- Chapter 14: Probability – Online Test
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